This 8-page article from Teaching Children Mathematics discusses how overgeneralizing commonly accepted practices, using imprecise vocabulary, and relying on tips and tricks that do not promote conceptual mathematical understanding can lead to misunderstanding later in students’ math careers. The authors provide a table of some "expired" mathematical language and suggest more appropriate alternatives.

This 46-page pdf document demonstrates the connections between the CCSS content standards and the mathematical practice standards. It is a compilation of research, standards from several states, instructional strategies, common misconceptions, and examples for each standard at the grade 1 level. It is intended to help teachers understand what each standard means in terms of what students must know and be able to do. Additional flip books are cataloged separately for grades K and 2-5.

This problem with multiple solutions offers an opportunity for students to practice simple addition and subtraction, work with number sentences (equations), and develop systematic work habits. Given cards containing the addition, subtraction and equal signs along with the digits 2, 4, 6, and 8. solvers are challenged to find as many ways as possible to arrange some or all seven cards to create true statements. The Teachers' Notes page offers suggestions for implementation, discussion questions, ideas for extension and support, printable cards (pdf) and a link to an interactive Flash applet.

In this 14-min video British teacher Rosalind Caren demonstrates group activities designed to develop number sense, fluency with addition and subtraction fact families, and reasoning skills. Caren exhibits effective questioning techniques and routines. Headteacher/math coordinator Kate Frood describes the guiding principles and expectations of teaching at the school. Following a class observation Frood provides constructive feedback to Caren and her teaching assistants.

This 8-page monograph explains bansho, a research-informed instructional strategy for mathematical communication and collective problem-solving. Following a brief overview, the article outlines how bansho can be used to plan and implement an effective three-part problem-solving lesson. Bansho can be incorporated into collaborative planning sessions, in which teachers work with partners or in groups within communities of practice to learn about mathematics for teaching. The author provides a sample grade 2 lesson on the development of multiplication concepts and a list of references.

This interactive Flash tool allows primary students to explore the concepts of equality and inequality with a balance. Learners receive cubes on both sides of a balance and must select from the given choices to determine the correct number of cubes to equalize the balance.

In this 6-lesson unit, students explore 5 models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using connecting cubes. The lesson activities focus on the comparative mode of subtraction as children investigate the relationship between addition and subtraction, write story problems in which comparison is required, and practice the subtraction facts. The lessons include printable student activity sheets, a bibliography of children's counting books, questions for student discussion and teacher reflection, assessment options, extensions, and links to online applets (cataloged separately).

This game from the BBC reinforces doubling and mental addition for a range of abilities. Students attempt to reach a target score by placing darts on the correct sections of a dartboard. The first level of the game provides practice doubling with a single number. Levels 2 and 3 increase the challenge level by involving two and three addends. Teachers and parents can control the starting level and the optional timing feature.

In this 6-lesson unit, students use dominoes to explore four models of addition: counting, number line, sets, and balanced equations. They learn about the commutative property, the relation between addition and subtraction, the result of adding 0, and the concept of doubles. Students write story problems which involve the operation of addition and begin to memorize the addition facts. They represent addition in pictures. The various models of addition help students develop a rich conceptual schema for addition. Included are a Bibliography of Counting Books, student materials, questions for student and teacher reflection, assessment and extension ideas. [Suggestion: Use the alternate applet, Pan Balance - Numbers, listed as a Related Resource, rather than Pan Balance - Shapes, in Lesson 4.]